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The work of Laurent Lafforgue

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Gérard Laumon

Number Theory · Submitted 1 Dec 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Laurent Lafforgue has been awarded the Fields Medal for his proof of the Langlands correspondence for the full linear groups $\mathop{\rm GL}\nolimits_{r}$ ($r\geq 1$) over function fields.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0212417 (version 1)
Pith ID2U3TNMXW, Pith's permanent record of this paper and its review
CitationG\'erard Laumon. "The work of Laurent Lafforgue." arXiv:math/0212417 (2002). https://pith.science/paper/2U3TNMXW
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,297 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.18 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Laurent Lafforgue has been awarded the Fields Medal for his proof of the Langlands correspondence for the full linear groups $\mathop{\rm GL}\nolimits_{r}$ ($r\geq 1$) over function fields. This article is a brief introduction to the Langlands correspondence and to Lafforgue's theorem.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Laurent Lafforgue has been awarded the Fields Medal for his proof of the Langlands correspondence for the full linear groups $\mathop{\rm GL}\nolimits_{r}$ ($r\geq 1$) over function fields. background 0.79 0.04 0.30 asserted 1.00
s1 This article is a brief introduction to the Langlands correspondence and to Lafforgue's theorem. contribution 0.85 0.15 0.05 asserted 0.92

What kind of paper the classifier reports this is: review 0.98 · evidence from literature 0.56.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Laurent Lafforgue has been awarded the Fields Medal for his proof of the Langlands correspondence for the full linear groups $\mathop{\rm GL}\nolimits_{r}$ ($r\geq 1$) over function fields. This article is a brief introduction to the Langlands correspondence and to Lafforgue's theorem.

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